Effects of oblateness of the primaries on natural periodic orbit-attitude behaviour of satellites in three body problem

Abstract

• Equations of Motion for the Perturbed Circular Restricted Three Body Problem (P-CR3BP) with considering A 2 - A 6 primaries oblate coefficients have derived for the first time. • It was shown that considering primaries zonal harmonic coefficients j 2 - j 6 has a significant effect on satellite orbit-attitude behavior. It is observed that considering A 2 - A 6 primaries oblate coefficients amplify the effect of oblate perturbations and the zonal harmonic coefficients after j 6 have negligible effect. • Proper initial guess of periodic solution of perturbed model identified by Poincaré maps. • As an innovation, finding the appropriate value of inertia ratio K to find periodic response of orbit-attitude was performed using Poincaré mapping for the first time. • It was shown for the first time, by more accurately simulating the study environment by considering oblate perturbations, the density of points on the islands created on Poincaré map appeared to increase, and in fact, it became easier to identify the initial guess of attitude states. • Increasing the inertia ratio and increasing the orbital period reduces the chances of finding periodic responses. This study was done to investigate the effect of perturbations of both oblate massive primaries on the periodic orbit-attitude behavior of satellites at the three-body problem. Governing equations of the perturbed coupled orbit-attitude were derived using principles of the Lagrangian mechanics. As initial conditions of the coupled model play a key role in finding periodic responses of both orbit and attitude, so the perturbed circular restricted three-body problem (P-CR3BP) coupled orbit-attitude correction algorithm was proposed to correct the initial guess of the coupled model. The correction algorithm requires an appropriate initial guess vector as the number of periodic solutions is limited. This initial guess vector consists of two parts: orbital and attitude dynamic state parameters. A suitable initial guess was suggested for orbital parameters considering a small error at the initial conditions of the unperturbed periodic orbits. These initial conditions were extracted by another orbital correction algorithm to correct orbital states of periodic orbits in the unperturbed circular restricted three-body problem (U-CR3BP). Furthermore, the initial guess of attitude dynamic parameters was identified by the Poincaré mapping method. Considering oblate perturbations would change the initial conditions of periodic orbits at P-CR3BP relative to U-CR3BP. Also, because the proposed model of the coupled orbit-attitude governing equations is such that only orbital state parameters influence attitude dynamic parameters, so the behavior of attitude dynamics will also change by altering orbital motion. Comparison of patterns in Poincaré maps, satellites angular velocity, and initial conditions of periodic coupled orbit-attitude response in U-CR3BP and P-CR3BP indicated the effect of both oblate primaries perturbations. Consideration of these perturbations resulted in a more accurate simulation of the study environment that helps to understand the natural motion of the satellite.